Geometry and trigonometry (IB)

Pythagorean theorem

a²+b²=c²

Volume of a cylinder

πr²h

Surface area of a cylinder

2πrh + 2πr²

Volume of a cone

1/3(πr²h)

Surface area of a cone

πrL + πr²

Volume of a sphere

4/3 (πr³)

Surface area of a sphere

4πr²

Volume of a pyramid

Base area × h × 1/3

Surface area of a pyramid

Add all faces

Sin x

Opp / hyp

Cos x

Adj / hyp

Tan x

Opp / adj

Sin rule

a/sinA = b/sinB = c/sinC

Cos rule

c²=a²+b² - 2ab cosC

Area of a triangle (with trigonometry)

½ ab sinC

Sin 30

½

Cos 30

√3/2

Tan 30

√3/3

Sin 45

√2/2

Cos 45

√2/2

Tan 45

1

Sin 60

√3/2

Cos 60

½

Tan 60

√3

Vertical symmetry in a unit circle

π-a

Horizontal symmetry in a unit circle

2π-a

Center symmetry in a unit circle

a +π

Sin² a + Cos²a

1

Cos 3a

4cos³a -3cosa

Sin 3a

3sina - 4sin³a

Sin 2a

2 sina cosa

Cos 2a

Cos²a - sin²a

2cos²a -1

1 - 2sin²a

Tan 2a

2tana/(1-tan²a)

Sina - sinb

2 sin (a-b/2) cos (a+b/2)

Sina + sinb

2 sin (a+b/2) cos (a-b/2)

Cosa + cosb

2 sin (a-b/2) cos (a+b/2)

Cosa - cosb

-2 sin (a+b/2) sin (a-b/2)

Cos(a+b)

Cosa cosb - sina sinb

Cos (a-b)

Cosa cosb + sina sinb

Sin (a+b)

Sina cosb + sinb cosa

Sin (a-b)

Sina cosb - sinb cosa

Arc length

Angle × r

Sector area

½ angle × r²